For the unsupervised learning problem, to recover true signal \(\mathbf {f}(t)\)  from anomaly-contaminated data, it is important to impose inductive bias or prior knowledge to the model as suggested in [1]}, [2]}. For time series modeling, we first introduce smoothness prior modeling of time series as described in [3]}. Consider the time series \(y_{1:T}\)  (for convenience, we deal with the uni-variate case), it is assumed to consist of the sum of a function \(f\)  and observation noise \(\epsilon \) :
\(y_t = f(t)+\epsilon _t\) 
